As a control device for a hybrid vehicle, for example, a device is per se known that, during stopping of an internal combustion engine of the vehicle, implements twist angle fluctuation reduction control in which amplification of twist angle fluctuations is suppressed by appropriately operating a motor-generator of the vehicle so that damping torque generated by the restoring force due to twisting of a torsional damper operates in the direction to cancel torque pulsations of the internal combustion engine during the stopping process (refer to Patent Document #1). Moreover, in some cases, in order to suppress vibration upon restarting of the internal combustion engine after it has been stopped, crank angle position control is performed in which, by appropriately operating the motor-generator, the crank angle is feedback controlled so that the internal combustion engine stops at a predetermined crank angle (for example, refer to Patent Document #2).